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OPTICS LETTERS / Vol. 32, No. 24 / December 15, 2007
Molecular tagging thermometry for transient
temperature mapping within a water droplet
De Huang and Hui Hu*
Aerospace Engineering Department, Iowa State University, Ames, Iowa 50011, USA
*Corresponding author: huhui@iastate.edu
Received August 28, 2007; revised October 22, 2007; accepted November 16, 2007;
posted November 21, 2007 (Doc. ID 86931); published December 10, 2007
We present the progress made in developing a molecular tagging thermometry (MTT) technique for achieving spatially and temporally resolved temperature measurements within a small water droplet over a solid
surface. For MTT measurement, a pulsed laser is used to tag phosphorescent 1-BrNp· M␤-CD· ROH molecules premixed with water. Long-lived laser-induced phosphorescence is imaged at two successive times
after the same laser excitation pulse. The temperature measurement is achieved by taking advantage of the
temperature dependence of the phosphorescence lifetime, which is estimated from the intensity ratio of the
acquired phosphorescence image pair. The measured transient temperature distributions can be used to
quantify the unsteady heat transfer process inside convectively cooled water droplets over smooth or rough
surfaces. © 2007 Optical Society of America
OCIS codes: 120.6780, 110.6820, 160.2540.
Aircraft icing is widely recognized as a significant
hazard to aircraft operations. Advancing the technology for safe and efficient aircraft operation in atmospheric icing conditions requires a better understanding of the microphysical phenomena associated
with the accretion and growth of ice. To elucidate underlying physics associated with aircraft icing, experimental techniques capable of providing detailed
measurements to quantify important ice growth
physical processes such as the dynamics of water
droplets and the unsteady heat transfer process inside water droplets over smooth or rough surfaces are
highly desirable. In this Letter, we report progress
made in our recent effort to develop and implement a
molecular tagging thermometry (MTT) technique to
achieve temporally and spatially resolved temperature measurements within small water droplets to
quantify the unsteady heat transfer process inside
convectively cooled water droplets over smooth or
rough surfaces for aircraft icing studies.
It is well known that both fluorescence and phosphorescence are molecular photoluminescence phenomena. Compared with fluorescence, which typically has a lifetime of the order of nanoseconds,
phosphorescence can last as long as microseconds,
even minutes. Since emission intensity is a function
of the temperature for some substances, both fluorescence and phosphorescence of tracer molecules may
be used for temperature measurements. Laserinduced fluorescence (LIF) techniques have been
widely used for temperature measurements of liquid
droplets for combustion applications [1–3]. Laserinduced phosphorescence (LIP) techniques have also
been suggested recently to conduct temperature measurements of in-flight or levitated liquid droplets
[4,5]. Compared with LIF techniques, the relatively
long lifetime of LIP could be used to prevent interference from scattered or reflected light, and any fluorescence from other substances (such as from solid
surfaces) that are present in the measurement area
by simply putting a small time delay between the la0146-9592/07/243534-3/$15.00
ser excitation pulse and the starting time for phosphorescence image acquisitions. Furthermore, LIP
was found to be three to four times more sensitive to
temperature variation compared with LIF [4–7],
which is favorable for accurate measurements of
small temperature differences within small liquid
droplets.
The MTT technique described at here is a LIPbased technique, which can be considered an extension of the molecular tagging velocimetry and thermometry technique developed by Hu and
Koochesfahani [6]. For MTT measurement, a pulsed
laser is used to tag a phosphor (e.g., phosphorescent
dye) premixed in the working fluid. The long-lived
LIP emission is imaged at two successive times after
the same laser excitation pulse. The LIP emission
lifetime distribution is estimated from the intensity
ratio of the acquired phosphorescence image pair.
The temperature distribution within a small water
droplet can be derived by taking advantage of the
temperature dependence of the phosphorescence lifetime. It should be noted that both the present MTT
measurement and the work of Omrane et al. [4,5] are
based on a similar idea of achieving temperature
measurement by taking advantage of the temperature dependence of the phosphorescence lifetime. The
work of Omrane et al. [4,5] is only a single-point feasibility study using photomuliplier-based instrumetation. The present work, to our knowledge, is the
first planar temperature field measurement to
achieve temporally and spatially resolved temperature measurement within a small water droplet
based on direct imaging of phosphorescence lifetime
with a conventional image-detecting CCD camera.
The technical basis of the MTT measurements is
given briefly here. According to quantum theory, the
intensity of phosphorescence emission decays exponentially. As described in [7], for a dilute solution and
unsaturated laser excitation, the phosphorescence
signal 共S兲 collected by using a gated imaging detector
with integration starting at a delay time to after the
© 2007 Optical Society of America
December 15, 2007 / Vol. 32, No. 24 / OPTICS LETTERS
3535
laser pulse and a gate period of ␦t can be given by
S = AIiC␧⌽p共1 − e−␦t/␶兲e−to/␶ ,
共1兲
where A is a parameter representing the detection
collection efficiency, Ii is the local incident laser intensity, C is the concentration of the phosphorescent
dye (the tagged molecular tracer), ␧ is the absorption
coefficient, and ⌽p is the phosphorescence quantum
efficiency. The emission lifetime ␶ refers to the time
at which the intensity drops to 37% (i.e., 1 / e) of the
initial intensity.
In general, the absorption coefficient ␧, quantum
yield ⌽p, and the emission lifetime ␶ are temperature
dependent, resulting in a temperature-dependent
phosphorescence signal 共S兲. Thus, in principle, the
collected phosphorescence signal 共S兲 may be used to
measure fluid temperature if the incident laser intensity and the concentration of the phosphorescent dye
remain constant (or are known) in the region of interest. It should be noted that the collected phosphorescence signal 共S兲 is also the function of incident laser
intensity 共Ii兲 and the concentration of the phosphorescent dye 共C兲. Therefore, the spatial and temporal
variations of the incident laser intensity and the nonuniformity of the phosphorescent dye in the region of
interest would have to be corrected separately to derive quantitative temperature data from the acquired
phosphorescence images. In practice, however, it is
very difficult, if not impossible, to ensure a nonvarying incident laser intensity distribution, especially
for unsteady thermal phenomena with a varying index of refraction. This may cause significant error in
the temperature measurements. To overcome this
problem, a lifetime-based thermometry [6] was developed to eliminate the effects of incident laser intensity and concentration of phosphorescent dye on temperature measurements.
The lifetime-based thermometry works as follows:
as illustrated in Fig. 1, laser-induced phosphorescence emission is interrogated at two successive
times after the same laser excitation pulse. The first
image is detected at time t = to after laser excitation
for a gate period ␦t to accumulate the phosphorescence intensity S1, while the second image is detected
at time t = to + ⌬t for the same gate period to accumulate the phosphorescence intensity S2. It is easily
shown, by using Eq. (1), that the ratio of these two
phosphorescence signals 共R兲 is given by
R = S2/S1 = e−⌬t/␶ .
Fig. 1. (Color online) Timing chart for MTT measurement.
A demonstration experiment was conducted to
implement the MTT technique described above. In
the present study, the phosphorescent triplex
共1-BrNp· M␤-CD· ROH兲 was used as the molecular
tracer for the MTT measurements. The phosphorescent triplex 共1-BrNp· M␤-CD· ROH兲 is actually the
mixture compound of three different chemicals [8],
which are lumophores (indicated collectively by
1-BrNp), maltosyl-␤-cyclodextrin (indicated by
M␤-CD), and alcohols (indicated collectively by
ROH). Figure 2 shows the measured phosphorescence lifetime of 1-BrNp· M␤-CD· ROH molecules
versus temperature with the laser excitation wavelength of 266 nm (quadrupled wavelength of the
Nd:YAG laser). It can be seen clearly that the phosphorescence lifetime varies significantly with increasing temperature, decreasing from about 3.4 to
1.5 ms as the temperature changes from 22° C to
36° C. The relative temperature sensitivity of the
phosphorescence lifetime is about 5.7% per degree
Celsius, which is much higher than those of fluorescent dyes [1–3] (such as Rhodamine B, which is only
about 2.0% per degree Celsius)
A water droplet with a size of about 10 mm and initial temperature of 32.5° C was placed on a test plate.
The temperature of the test plate was set as the same
as that of ambient air, which was 23.5° C. The water
droplet was convectively cooled after it was placed on
the test plate. A laser sheet (1.0 mm in thickness)
from a pulsed Nd:YAG laser at a quadrupled wavelength of 266 nm was used to tag the premixed
共2兲
In other words, the intensity ratio of the two successive phosphorescence images 共R兲 is a function of only
the phosphorescence lifetime ␶ and the time delay ⌬t
between the image pair, which is a controllable parameter. This ratiometric approach eliminates the effects of any temporal and spatial variations in the incident laser intensity and nonuniformity of the dye
concentration (e.g., due to bleaching). For a given molecular tracer and fixed ⌬t value, Eq. (2) defines a
unique relation between phosphorescence intensity
ratio R and fluid temperature T, which can be used
for thermometry.
Fig. 2. Phosphorescence lifetime versus temperature.
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OPTICS LETTERS / Vol. 32, No. 24 / December 15, 2007
Fig. 4.
(Color
distribution.
Fig. 3. (Color online) Typical phosphorescence image pair.
1-BrNp· M␤-CD· ROH molecules along the mid plane
of the water droplet. A 12 bit gated intensified CCD
camera (PCO DiCam-Pro) with a fast decay phosphor
(P46) was used to capture the phosphorescence emission. The camera was operated in the dual-frame
mode, where two full-frame images of phosphorescence were acquired in quick succession after the
same laser excitation pulse. Figure 3 shows a typical
phosphorescence image pair, which was acquired
about 45 s after the water droplet was placed on the
test plate. The first image was acquired at 0.4 ms after the laser pulse, and the second image at 4.9 ms
after the same laser pulse with the exposure time of
1.5 ms for the two image acquisitions. Since the time
delays between the laser excitation pulse and the
phosphorescence image acquisitions eliminated scattered or reflected light and any fluorescence from
other substances (such as from solid surfaces) effectively, the phosphorescence images of the water droplet are quite clean. Figure 4 shows the instantaneous
temperature distribution within the water droplet
derived from the phosphorescent image pair shown
in Fig. 3. Because of the relatively high temperature
sensitivity of the present MTT technique, the small
temperature difference within the water droplet
could be revealed clearly from the MTT measurement. As it is expected, the surface temperature of
the water droplet was found to decrease rapidly to
online)
Instantaneous
temperature
ambient air temperature. The bottom temperature of
the water droplet was found to be slightly higher
than ambient air temperature owing to the low thermal conductivity of the plastic test plate. Based on
the time sequence of the measured transient temperature distributions within the water droplet, the
unsteady heat transfer process inside the convectively cooled water droplets can be revealed quantitatively. Such information is highly desirable to improve
our
understanding
of
microphysical
phenomena associated with the accretion and growth
of ice for aircraft icing studies.
The authors thank Manoochehr Koochesfahani of
Michigan State University for providing chemicals
used for the present study. The support of National
Science Foundation CAREER program under award
number CTS-0545918 is gratefully acknowledged.
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